E=1+3+32+33+...+3n
ai làm dk mk tick cho
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Ta có:
\(1+3+3^2+3^3+...+3^{99}\)
\(\Rightarrow3S=3+3^2+3^3+3^4+...+3^{99}+3^{100}\)
\(\Rightarrow3S-S=\left(3+3^2+3^3+...+3^{100}\right)-\left(1+3+3^2+...+3^{99}\right)\)
\(\Rightarrow2S=3^{100}-1\)
\(\Rightarrow2S+1=3^{100}-1+1=3^{100}\)
\(\Rightarrow2S+1\) là lũy thừa của 3
32 + 33 + 32 + 33 + 32 + 33 + 332 + 333 + 332+ 333 + 3332 + 3333 = 8190
Ta có: `B = 1 + 3 + 3^2 + ... + 3^1991`
`= (1 + 3 + 3^2) + (3^3 + 3^4 + 3^5) + ... + (3^1989 + 3^1990 + 3^1992)`
`= 13 + 3^3 (1 + 3 + 3^2) + ... + 3^1989 (1 + 3 + 3^2)`
`= 13 + 3^3 . 13 + ... + 3^1989 . 13`
`= 13 (1 + 3^3 + ... + 3^1989)`
Vì \(13\left(1+3^3+...+3^{1989}\right)⋮13\) nên \(B⋮13\)
`B = 1 + 3 + 3^2 + ... + 3^1991`
= (1 + 3^4) + (3 + 3^5) + ... + (3^1987 + 3^1991)`
`= 82 + 3 (1 + 3^4) + ... + 3^1987 (1 + 3^4)`
`= 82 + 3 . 82 + ... + 3^1987 . 82`
`= 82 (1 + 3 + ... + 3^1987)`
Vì \(82\left(1+3+...+3^{1987}\right)⋮41\) nên \(B⋮41\)
`C = 3 + 3^2 + 3^3 + ... + 3^1000`
\(=\left(3+3^2+3^3+3^4\right)+\left(3^5+3^6+3^7+3^8\right)+...+\left(3^{997}+3^{998}+3^{999}+3^{1000}\right)\)
`= 120 + 3^4 (3 + 3^2 + 3^3 + 3^4) + ... + 3^996 (3 + 3^2 + 3^3 + 3^4)`
`= 120 + 3^4 . 120 + ... + 3^996 . 120`
`= 120 (1 + 3^4 + ... + 3^996)`
Vì \(120\left(1+3^4+...+3^{996}\right)⋮120\) nên \(C⋮120\)
Ta có: \(C=3+3^2+3^3+...+3^{1000}\)
\(=\left(3+3^2+3^3+3^4\right)+\left(3^5+3^6+3^7+3^8\right)+...+\left(3^{997}+3^{998}+3^{999}+3^{1000}\right)\)
\(=120\left(1+3^5+...+3^{997}\right)⋮120\)(đpcm)
\(a,\dfrac{2}{5}+\dfrac{3}{4}:2=\dfrac{2}{5}+\dfrac{3}{8}=\dfrac{16}{40}+\dfrac{15}{40}=\dfrac{31}{40}\)
\(b,\dfrac{1}{2}\times\left(\dfrac{5}{2}-\dfrac{3}{5}\right)=\dfrac{1}{2}\times\dfrac{19}{10}=\dfrac{19}{20}\)
a: =2/5+3/8=16/40+15/40=31/40
b: =1/2x(25/10-6/10)
=1/2x19/10=19/20
a) -23.63 + 23.21-58.23
=-1449+483-1334
=-966-1334
=-2300
b) (-67).75 + 75.(-33)
=75.[-67+(-33)]
=75.(-100)
=-7500
c)(-5).8.(-2).3
=-40.(-6)
=240
d) (-163)+177+263-377
=[(-163) + 263] + (377-177)
=100+200
=300
e) (-2)^4.17+(-7).16
=-16.17+(-112)
=-272+(-112)
=-384
f) 125-(-75) + 32-(48+32)
=87 + 32-80
=87-80+32
=7+32
=39
E = 1 + 3 + 32 + 33 + ... + 3n
E = 30 + 31 + ... + 3n
3E = 31 + 32 + ... + 3n+1
3E - E = (31 + 32 + ... + 3n+1) - (30 + 31 + ... + 3n)
2E = 31 - 31 + 32 - 32 + ... + 3n-1 - 30
2E = 3n-1 - 30
E = ( 3n-1 - 1) : 2
Hãy k cho mk nhé
Đề bài???